Use the remainder Theorem to find the remainder for (x2- 2)/(x - 1) and state whether or not the binomial is a factor of
       
      
                
     
    
    
    
    
    1 answer:
            
              
              
                
                
Answer:
The remainder is -1
The binomial is not a factor of the polynomial
Step-by-step explanation:
In the algebraic division, there are 4 terms
- Dividend ⇒ the term before the division sign
- Divisor ⇒ the term after the division sign
- Quotient ⇒ the answer
- Remainder ⇒ appear when the dividend not divisible by the divisor (the divisor is not a factor of the dividend)
<u><em>The remainder theorem:</em></u>
- If you divide a polynomial f(x) by (x - h), then the remainder is f(h).
- You do not need to use the long division to find the remainder, just evaluate the polynomial when x = h to find the remainder.
- If h(h) = 0, then (x - h) is a factor of f(x)
Let us use it to solve the question
∵ The dividend is x² - 2
∴ f(x) = x² - 2
∵ The divisor is x - 1
∴ (x - h) = (x - 1)
∴ h = 1
Let us find f(1)
∵ f(1) = (1)² - 2 = 1 - 2 = -1
∴ f(1) = -1
∴ The remainder is -1
∵ f(1) ≠ 0
∴ x - 1 is not a factor of x² - 2
∴ The binomial is not a factor of the polynomial
 
                                
             
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